I'm probably not able to mentor this summer, but I will note that Sage does include point counting on hyperelliptic curves using p-adic methods (https://doc.sagemath.org/html/en/reference/arithmetic_curves/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.html). Certainly there's always more that can be done in terms of optimization.
There is an old ticket related to optimized arithmetic in Jacobians of hyperelliptic curves (https://trac.sagemath.org/ticket/23154), one on exposing the matrix of Frobenius from Pari (https://trac.sagemath.org/ticket/20309) and some related bugs (https://trac.sagemath.org/ticket/32024) that may be interesting to look at. David On Wednesday, April 7, 2021 at 5:30:49 PM UTC-4 Simon Schwarz wrote: > Hello all, > > my name is Simon and I am currently a postgraduate student in Computer > Science at the University of Cambridge. > > As a GSoC 2021 project, I would be interested in extending SageMath's > implementation of Jacobians of hyperelliptic curves. In particular, I'd > like to add point counting methods over finite fields (relevant paper > <https://hal.inria.fr/inria-00512403/document>) and implement the Weil > pairing (and possibly additional pairings) on hyperelliptic curves (relevant > paper <http://cacr.uwaterloo.ca/techreports/2009/cacr2009-30.pdf>). > Note that SageMath already supports those over elliptic curves, but > currently lacks support for hyperelliptic curves. In contrast, Magma > already includes those methods (see Magma documentation here > <https://magma.maths.usyd.edu.au/magma/handbook/text/1557>), so I think > it would be a great addition if this functionality is also supported by > SageMath. > > If anybody can imagine being a mentor for this project please get in touch > with me so we can discuss this project a bit further. Likewise, if you have > any other questions do not hesitate to contact me. > > Best regards, > Simon > -- You received this message because you are subscribed to the Google Groups "sage-gsoc" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-gsoc/1da23d4b-27b2-4b2f-bdbe-74698da784e7n%40googlegroups.com.
